Elena B. Aleksandrova

Asymptotic Stability Conditions and Estimates of Solutions for Nonlinear Multiconnected Time-Delay Systems

This paper examines certain classes of multiconnected (complex) systems with time-varying delay. Delay-independent stability conditions and estimates of the convergence rate of solutions to the origin for those systems are derived. It is shown that the exponents in the obtained estimates depend on the parameters of Lyapunov functions constructed for the corresponding isolated subsystems. The problem of computing parameter values that provide the most precise estimates is investigated. Some examples are presented to demonstrate the effectiveness of the proposed approaches.

Ultimate boundedness conditions for a hybrid model of population dynamics

This paper addresses the ultimate boundedness and permanence analysis for a Lotka-Volterra type system with switching of parameter values. Two new approaches for the constructing of common Lyapunov function for the family of subsystems corresponding to the switched system are suggested. Sufficient conditions in terms of linear inequalities are obtained to guarantee that the solutions of the considered system are ultimately bounded or permanent for an arbitrary switching signal. An example is presented to demonstrate the effectiveness of the proposed approaches.

Stability analysis of some classes of nonlinear switched systems with time delay

ABSTRACT Stability of certain classes of nonlinear time-delay switched systems is studied. For the corresponding families of subsystems, conditions of the existence of common Lyapunov–Razumikhin functions are found. The fulfilment of these conditions provides the asymptotic stability of the zero solutions of the considered hybrid systems for any switching law and for any nonnegative delay. Some examples are presented to demonstrate the effectiveness of the obtained results.

Stability analysis and estimation of the convergence rate of solutions for nonlinear time-delay systems

Certain classes of systems with nonlinearities of a sector type and time-varying delay are studied. By the use of the Lyapunov functions method and the Razumikhin approach, conditions are obtained under which the zero solution of considered systems is asymptotically stable for an arbitrary continuous nonnegative and bounded delay. Moreover, estimates of the convergence rate of solutions are derived.

Delay-independent stability conditions for a class of nonlinear difference systems

Abstract The paper addresses the asymptotic stability problem for a class of difference systems with nonlinearities of a sector type and time-delay. A new approach to Lyapunov–Krasovskii functionals constructing for considered systems is proposed. On the basis of the approach, delay-independent asymptotic stability conditions and estimates of the convergence rate of solutions are derived. In addition, stability of perturbed systems is investigated in the case where nonstationary perturbations admit zero mean values. Some examples are given to illustrate the obtained results.

Convergence conditions for some classes of nonlinear systems

Abstract Systems of differential equations with nonlinearities of a sector type and almost periodic perturbations are studied. With the aid of the Lyapunov direct method, conditions are found under which the considered systems admit globally asymptotically stable almost periodic solutions. Moreover, it is shown that the proposed approach permits us to derive new convergence conditions for some models of neural networks and generalized Lotka–Volterra models of population dynamics. An example is presented to demonstrate the effectiveness of the obtained results.

Estimate of the attraction domain for a class of nonlinear switched systems

We consider a hybrid dynamical system composed of a family of subsystems of nonlinear differential equations and a switching law which determines the order of their operation. It is assumed that subsystems are homogeneous with homogeneity degrees less than one, and zero solutions of all subsystems are asymptotically stable. Using the Lyapunov direct method and the method of differential inequalities, we determine classes of switching laws providing prescribed estimates of domains of attraction for zero solutions of the corresponding hybrid systems. The developed approaches are used for the stabilization of a double integrator.

Stability analysis and estimation of the attraction domain for a class of hybrid nonlinear systems

A switched system generated by the family of homogeneous subsystems with homogeneity orders less than one is studied. It is assumed that the zero solution of each subsystem is asymptotically stable. On the basis of the dwell-time approach, conditions on switching law are determined under which a given spherical neighborhood of the origin is contained in the attraction domain of the zero solution of the corresponding hybrid system.